Respuesta :
Using the Poisson distribution, the probability of observing exactly three accidents on this stretch of road next month is given by:
b) 0.052.
What is the Poisson distribution?
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
- x is the number of successes
- e = 2.71828 is the Euler number
- [tex]\mu[/tex] is the mean in the given interval.
Researching this problem on the internet, the mean is given by:
[tex]\mu = 7[/tex].
The probability of observing exactly three accidents on this stretch of road next month is P(X = 3), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-7}7^{3}}{(3)!} = 0.052[/tex]
Hence option B is correct.
More can be learned about the Poisson distribution at https://brainly.com/question/13971530
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